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Find the solution of the differential equation that satisfies the given initial condition.$ \frac {du}{dt} = \frac {2t + \sec^2t}{2u}, u(0) = 0 $

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$u=-\sqrt{t^{2}+\tan t+25}$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

Matt S.

October 23, 2021

Why no plus/minus?

Campbell University

University of Nottingham

Boston College

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

33:32

02:35

Find both the general solu…

00:55

Find the solution of the d…

01:50

00:49

01:19

Use separation of variable…

0:00

Solve the differential equ…

01:18

First find the general sol…

06:17

this question asked us to find the solution of the differential equation that satisfies the given additional condition. We know we have d'you over G is two teeth plus sequence where team divide by to you. Now let's get all the you terms on left inside to you D you and all the ti terms on the right hand side because it will make it significantly easier to integrate. Take the integral of both sides. Tiu to you becomes you squared because we increase the exploited by one and we divide by the new exponents. Marco, fishing just becomes one or two over too. On the right hand side, we have cheese squared plus tan of team plus c Remember, the integral seeking scored of tea is 10 of tea. Now that we have this, we know we're gonna be substituting. And if you have zero is negative five than t zero and use negative five substitute in. Remember, we're solving for C. We got C is 25. Lastly, plug back in to our equation that we determined once we integrated the sea is 25 instead of plus C, we now have plus 25 then take the squirt of both sides. Because we want this in terms of singular. You not. You squared and we end up with our solution. So this is all under the square root now?

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